Given the alphabet $\{0,1\}$, generate a regular expression with the following language: $$ \{w\in \Sigma^* \mid w \text{ has odd length and its middle symbol is }1\}. $$
I'm having trouble finding a solution for this regular expression. I think it's impossible because you need to have an even amount of 1's and 0's on both sides of the middle 1. You also would need to have the same amount of 1's and 0's on both sides. Since a regular expression has limited memory, would that make this regular expression impossible?